Manipulatives – Making Math FunDr. Laura Taddei

Learning Outcomes

• Discuss ways to enhance children’s natural interest in mathematics and disposition towards mathematics

• Actively engage in mathematical concepts, methods, and language through a range of appropriate experiences and teaching strategies

• Develop, implement, assess and modify curriculum and lessons using the PA Learning Standards

Math and Anxiety

• Abbreviated Mathematics Anxiety Rating Scale (A-Mars) Questionnaire Abbreviated version of Mathematics Anxiety Rating Scale http://www.pearweb.org/atis/tools/58

• How do you feel about mathematics? • Gresham (2007) conducted a study on pre-service

teachers level of anxiety regarding mathematics

Bruner’s Theory

• Applying Bruner’s theory of developing conceptual knowledge before procedural knowledge – discovery learning

• Using manipulatives and other materials – make concepts more concrete and meaningful

• Data revealed a statistically significant reduction in math anxiety when Bruner’s theory was implemented (Gresham, 2007)

• http://www.simplypsychology.org/bruner.html

How to Relieve Math Anxiety

• Use manipulatives • Encourage small group discussions• Journal Writing• Literature Based Math Activities

• Young children learn by being actively involved• To be good or proficient at mathematics, children must

know more than the content.• Children should be given opportunities to communicate

and connect knowledge to other mathematical ideas and to other subject areas, represent their understanding, solve problems and reason, and demonstrate a disposition to think flexibly

Process Standards

• Problem solving• Reasoning• Communication• Connections• Representation• Process Standards from NCTM

Identify the Process Standards

• Please watch the video and identify process standards (as identified by the NCTM) being used.

• Math Instruction in a Seattle Public School

• Teacher’s role in the classroom• When watching this video, how do the teachers describe

their role in teaching math in the classroom - Everyday Math

Manipulative Small Group Activity

• You will be working in small groups with a hands-on math activity

• After completing the activity, please identify what your group decides is the goal of the activity (what is the big idea), the grade level this activity would be appropriate for, and at least five ways you could implement the process standards.

• PA Common Core Standards for Math

Helping Children Problem-Solve

Understand the problem• Experience with material • Prior knowledge

Planning how to solve it• Prior knowledge

Carrying out the plan• Modify• Try again

Reviewing the solution

Promoting Reasoning Skills

Ask question that require investigation and reasoning. • Are you sure?• How do you know?• Why do you think …?• What else can you find that works like this?• What would happen if …?• I wonder how this could be changed?• What would the pattern be …?• What if …?• I wonder why …?• Perhaps it’s because …?

Promoting Communication Skills

• Teacher’s can verbalize and restate mathematical concepts and process and ask questions to help children clarify or extend their ideas

• Also to help give them a lot of opportunities to talk with and listen to their peers

Promoting Connections

• The overall goal is understanding: if they can see how it is related or connected to other things they know

Promoting Representation

• To encourage flexibility in mathematical representation use – pictorial (drawings, maps), graphical (bar graphs made from stacked objects, timelines, pictographs), and symbolic (tables, prose descriptions).

• Provide Opportunities to talk about Mathematics• Build In Opportunities for Reflective Thought• Encourage Multiple Approaches• Teaching should provide opportunities for students to

build connections between what they know and what they are learning.

• Engage Students in Productive Struggle• Allow students the time to struggle with the mathematics

they are exploring.

• Treat Errors as Opportunities for Learning• Scaffold New Content• For concepts completely new to students, the learning

requires more structure or assistance, including the use of tools like manipulatives or more assistance from peers.

• Honor Diversity• Each learner is unique, with a different collection of prior

knowledge and cultural experiences. Since new knowledge is build on existing knowledge and experience, effective teaching incorporates and builds on what the students bring to the classroom.

Questions or Comments

Please contact Laura Taddei at Ltaddei@mc3.edu if you have any questions or comments.

Resources

Enterprise School (2011) provided an article An Entrepreneurial Development Framework for Higher Education

Institutions. Extracted from

http://www.jadeportugal.org/an-entrepreneurial-development-framework-for-institutions-of-higher-education.html

Reimers-Hild & King (2009). Six questions for entrepreneurial leadership and innovations in distance education. Online

Journal of Distance Learning Administration. Extracted from http://www.westga.edu/~

distance/ojdla/winter124/reimers-hild124.html

Ryshke, R. (2012) What schools can do to encourage innovation. Extracted from

http://rryshke.wordpress.com/2012/02/26/what-schools-can-do-to-encourage-innovation/

Simmons, E. (2012) Rewarding Teaching Innovations. Extracted from

http://www.insidehighered.com/advice/2012/04/18/essay-how-colleges-can-encourage-professors-innovate-teaching